CN109446634A - Ship movement prediction method based on Taylor expansion Element BEM - Google Patents
Ship movement prediction method based on Taylor expansion Element BEM Download PDFInfo
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Abstract
The present invention is to provide the ship movement prediction methods based on Taylor expansion Element BEM.Grid file is read, hydrostatic calculation is carried out；The influence coefficient matrix of boundary integral equation needed for calculating Taylor expansion Element BEM；Folded mould velocity potential and its space one, second dervative and Mj solve；Time domain Green function and its space normal derivative solve；The instantaneous item of radiation velocity gesture and its space one, second dervative solve；Radiation velocity gesture memory term and its space one, second dervative solve；Additional mass, wave making damping, radiation wave force impulse response function solve；Incidence rate gesture impulse response function solves full wave downwards；Diffraction velocity potential and its space one, second dervative, diffraction wave force impulse response function solve；Full wave moves solution to ship；Ship movement spectrum analysis calculates under sea situations at different levels.The present invention can forecast that the hydrodynamic force coefficient of three big main force's ship types, seaway load, full wave are moved to ship 6 degree of freedom, and ship moves spectrum analysis under sea situations at different levels.
Description
Technical field
The present invention relates to a kind of analogy method, it is especially a kind of using Taylor expansion Element BEM calculate it is permanent and
The method of each unsteady velocity potential impulse response function, and then forecast that full wave moves RAO to three-dimensional ship.
Background technique
Ship seakeeping is all the important ship performance index of Ship Design personnel concern all the time, to the safety of cargo
Property, passenger comfort, ship energy consumption all have a major impact.But exploitation is suitble to the three-dimensional ship Motion prediction software of any ship type
It is still hydrodynamics Research Challenges.
Container ship tail portion is big flare ship type, and using the solution of time domain Green function method, there are numerical divergences to ask
Topic.Forecast domain is all made of Simple Green Function method when therefore moving for big flare ship type.The Block Coefficient of oil carrier and bulk freighter
Larger, i.e., so-called fat type ship needs to consider permanent folded mould gesture to unsteady in the type ship Motion prediction numerical simulation
The influence of velocity potential.Therefore Free Face Conditions implementation logarithm forecast precision also has an impact.Currently used Free Face Conditions packet
Include NK Free Face Conditions and DB Free Face Conditions.Because DB Free Face Conditions design the calculating of folded mould gesture second dervative,
It is more complicated than NK Free Face Conditions.And wedge angle boundary velocity potential second dervative accurately solve be numerical simulation difficult point.
Ship form optimization design needs a set of method for capableing of Fast Prediction ship performance, and can differentiate different bows, water
The influence of the parameter logs such as line, Block Coefficient forecast.Therefore the computational efficiency of numerical method is just particularly important.And it needs
Distinguish the influence of each ship type parameter, therefore numerical method is three-dimensional.
Summary of the invention
The purpose of the present invention is to provide one kind can the full wave of Fast Prediction it is main greatly to oil carrier, bulk freighter and container ship three
The ship movement prediction method based on Taylor expansion Element BEM of power ship type movement.
The object of the present invention is achieved like this:
Step 1, grid file is read, carries out ship hydrostatic calculation using gridding information；
Step 2, influence coefficient matrix involved in boundary integral equation needed for calculating Taylor expansion Element BEM；
Step 3, it folds mould velocity potential and its space single order, second dervative and Mj solves；
Step 4, time domain Green function and its space normal derivative solve；
Step 5, the instantaneous item of radiation velocity gesture and its space single order, second dervative solve；
Step 6, radiation velocity gesture memory term and its space single order, second dervative solve；
Step 7, additional mass, wave making damping, radiation wave force impulse response function solve；
Step 8, incidence rate gesture impulse response function solves full wave downwards；
Step 9, diffraction velocity potential and its space single order, second dervative, diffraction wave force impulse response function solve；
Step 10, full wave moves RAO to ship and solves；
Step 11, ship movement spectrum analysis calculates under sea situations at different levels.
For three big main force's ship types (oil carrier, bulk freighter and container ship) in bow tail portion, there is wedge angle in the turn of the bilge.Therefore accurate
The second dervative of the folded mould gesture of solution wedge angle boundary, radiation velocity gesture memory term and diffraction velocity potential is the key that numerical simulation.
The present invention can accurately solve the second dervative of any Basin Boundary using Taylor expansion Element BEM.Impulse response function side
Method can the movement of Fast simulation ship.In conjunction with this two o'clock, the invention proposes the Taylor expansion boundary element sides of coupled pulse receptance function
Method.
It is capable of the hydrodynamic force coefficient of the big main force's ship type of Fast Prediction three using method proposed by the present invention, seaway load, entirely
Wave is moved to ship 6 degree of freedom, and ship moves spectrum analysis under sea situations at different levels.
Detailed description of the invention
Fig. 1 is flow chart of the invention.
Specific embodiment
It illustrates below and the present invention is described in more detail.
1) it reads grid file and automatically extracts ship waterline information (including head and the tail stationary point space coordinate, waterline matched curve
Function).In conjunction with flow field matching boundary wisdom parameter and waterline information, the water surface and the matching face of coincidence boundary member method are automatically generated
Discrete grid block.And it is based on hull discrete grid block, Ship ' displacement of volume, centre of buoyancy, the centre of floatation, the moment of inertia, the hydrostatic such as wetted surface area
Force parameter.The error for checking hydrostatic force parameter numerical result and physics ship parameter, examines ship mesh quality with this.
2) present invention utilizes each velocity potential ingredient of Taylor expansion Solution of Boundary Element Method and its space single order, second dervative.Taylor
Expansion core concept is the method that the boundary integral equation formed based on Green's third formula carries out numerical discretization solution.For three
Dimension problem takes cell node coordinate equal for several quadrangles or triangular element for wetted surface of floating body is discrete on each unit
Centered on value, at face element midpoint, antithesis pole strength makees Taylor expansion and retains first derivative item, makees Taylor expansion to source strength and only protects
Stay first derivative item.And the tangential first derivative for introducing site carrys out Closure equation group, to constitute strong about dipole intensity, idol
First derivative be unknown number, source strength be known variables linear algebraic equation systems.The wherein influence of even strong tangential first derivative
Coefficient includes main value (being positive/negative half after normalization).What aforesaid operations method generated solves boundary using boundary element
The method of Integral Equation Solution is known as Taylor expansion Element BEM.Any face element i can be obtained single order simplified as follows
The discrete equation group of Taylor expansion Element BEM, i=1,2 ..., N,
Element expression in each matrix of above formula:
In formula: superscript i and j indicate bin number.An explanation is done by taking element expression a certain in matrix as an example: such as:
This method can simultaneously solving speed gesture and two mutually orthogonal tangential direction derivatives.Using object plane normal direction can not
Condition is penetrated, that is, constitutes the velocity field of local local coordinate system.Velocity field can be achieved under local coordinate and earth coordinates
Under conversion.Numerical result proves that this method can obviously improve the computational accuracy of the tangential induced velocity of Basin Boundary corner.
Introduce auxiliary functionThe space of φ is solved using Taylor expansion Element BEM again, i.e. velocity potential space second order is led
Number.Therefore this method is related to several influence coefficient matrixs calculating.
3) general speed gesture can be analyzed to steady velocity gesture, unsteady incident gesture, radiation velocity gesture and diffraction velocity potential.That is:
Steady velocity gesture can be analyzed to speed of incoming flow gesture and folded mould velocity potential again, it may be assumed that
Φb=-Ux+ Φ (3)
The object plane condition of unsteady gesture Definite problem, which is related to permanent gesture, to be influenced, i.e. and mj.For DB it is assumed that its boundary values solves surely
Problem are as follows:
Based on DB linear hypothesis mj are as follows:
In formula:For the displacement at object plane each point.For hull translation
Displacement,For hull rotation displacement,For various point locations radius vector on hull wet structure.
4) present invention disturbs wave using matching method unofficial biography, utilizes time domain Green function construction matching item on the mating surface
Part.Time domain Green function are as follows:
5) radiation potential can be analyzed to temporal effect part ψiWith memory effect part χi:
Wherein δ (t) and H (t) is respectively impulse function and jump function.Formula (8) and (9) are that the instantaneous item of radiation potential determines solution
Problem, two Definite problems utilize Taylor expansion Element BEM to solve.
6) Definite problem of radiation velocity gesture memory term such as formula (10) is solved using Taylor expansion boundary element method time stepping
The initial boundary problems.
The expression formula of Free Face Conditions right-hand vector F is expressed as follows in formula:
Using the velocity potential of each discrete unit center on the Integration Scheme Free Face Conditions stepping scope of freedom.With any letter
For number f (t), illustrates the core concept of Integration Scheme Free Face Conditions: time quadratic integral being made to integrand.
Similarly make time quadratic integral to Free Face Conditions to obtain:
Integration Scheme Free Face Conditions are calculated using trapezoidal method.To realize the stepping of Free Face Conditions time.
7) after the completion of the instantaneous item of radiation velocity gesture and memory term and its space derivation calculate, ship can be carried out and add matter
Amount, wave making damping calculate.
In formula: Aij(ω), Bij(ω) respectively indicates ship additional mass and wave making damping under corresponding wave frequencies ω.
8) radiation velocity gesture solution finishes, and can carry out the solution of diffraction velocity potential.It needs to solve first before diffraction velocity potential complete
Unrestrained ship incidence wave velocity potential downwards and incident wave force.Because the object plane condition in diffraction velocity potential Definite problem be related into
Penetrate velocity potential.In ship 6 degree of freedom movement solves, wave-excited force is also related to incidence rate gesture.For there is speed of a ship or plane problem,
Incident wave is divided into head sea and is handled respectively with stern sea two parts.
For heading sea, wave frequencies and experience frequency are one-to-one relationships, and there is no need to segment processings.It heads sea operating condition,
Incidence rate gesture impulse response function are as follows:
It heads sea operating condition, incident wave force impulse response function:
For stern sea, wave frequencies and experience frequency are being not one-to-one relationships, it is therefore desirable to segment processing, so that wave
Unrestrained frequency and experience frequency are monotone variation relationship on each piecewise interval.From experience frequency calculation formula, piecewise interval
Are as follows: (0, g/2ucos β), (g/2ucos β, g/ucos β), (g/ucos β, ∞).On each piecewise interval, incidence rate gesture pulse
Receptance function are as follows:
Stern sea operating condition, according to the orthogonality of Fourier transformation, incident wave force impulse response function function are as follows:
9) diffraction velocity potential and incidence rate are bound to unanimously, therefore to be also required to be decomposed into and head sea and stern sea two parts.But
Respective Definite problem is almost the same, only difference is that corresponding object plane condition is different, need to utilize the incidence of respective subregion
Velocity potential impulse response function.Diffraction velocity potential impulse response function Definite problem are as follows:
Free Face Conditions also use Integration Scheme Free Face Conditions, and principle is similar to formula (12).Diffraction speed is solved
Potential function, diffraction wave force impulse response function function are as follows:
10) incident and diffraction wave force impulse response function solution finishes, and can be exchanged into time-domain signal:
And then obtain wave force.(additional mass, wave making damping are infinite for the hydrodynamic force derivatives in conjunction with caused by radiation velocity gesture
Big frequency additional mass, time delay function), full wave can be carried out and calculated to six free movement of ship.The ship 6 degree of freedom equation of motion
Are as follows:
C in formulaijFor ship self-recovery force coefficient.The equation of motion is solved using fourth-order Runge-Kutta method stepping.
11) after obtaining ship 6 degree of freedom movement RAO, ship under sea situations at different levels can be obtained using spectral analysis method and is moved
Amplitude.The two-parameter spectrum of ITTC is shown below:
Wherein, T1To compose the heart period；H1/3For ariyoshi wave height, ω is circular frequency, and S (ω) is wave spectrum density.Freely by six
Degree movement RAO value brings spectrum analysis formula into, just obtains motion amplitude of the ship in practical sea situation
The features of the present invention is embodied in:
1. in step 1, in conjunction with Ship's Principal Dimensions and ship waterline Automatic generation of information, forming pulse matching boundary element side
Basin discrete grid block needed for method.
2. step 3, corresponding folded mould gesture in 4,5,6,9, the instantaneous item first part of radiation potential, second part, radiation potential note
Recall item, diffraction gesture and its space derivation utilize Taylor expansion Element BEM to solve.
3. corresponding radiation potential memory term and diffraction gesture impulse response function time domain solve in step 6 and 9, free noodles
Part uses DB format, i.e. influence of the consideration Steady Flow to unsteady gesture.
4. corresponding radiation potential memory term and diffraction gesture impulse response function time domain solve in step 6 and 9, free noodles
Part uses Integration Scheme, so that time step and mesh scale meet numerical discretization requirement.
5. step 3, corresponding folded Model Potential in 4,5, the corresponding boundary integral equation of the instantaneous item of radiation potential utilize GMRES
(m) solution by iterative method improves computational efficiency.
6. radiating the boundary integral equation solved with diffraction gesture in step 6 and 9, time stepping is carried out using matrix inversion method
It solves.Inverse matrix is solved to be accelerated parallel using OpenMP, improves computational efficiency.
Claims (9)
1. a kind of ship movement prediction method based on Taylor expansion Element BEM, it is characterized in that including the following steps:
Step 1, grid file is read, carries out ship hydrostatic calculation using gridding information；
Step 2, influence coefficient matrix involved in boundary integral equation needed for calculating Taylor expansion Element BEM；
Step 3, it folds mould velocity potential and its space single order, second dervative and Mj solves；
Step 4, time domain Green function and its space normal derivative solve；
Step 5, the instantaneous item of radiation velocity gesture and its space single order, second dervative solve；
Step 6, radiation velocity gesture memory term and its space single order, second dervative solve；
Step 7, additional mass, wave making damping, radiation wave force impulse response function solve；
Step 8, incidence rate gesture impulse response function solves full wave downwards；
Step 9, diffraction velocity potential and its space single order, second dervative, diffraction wave force impulse response function solve；
Step 10, full wave moves RAO to ship and solves；
Step 11, ship movement spectrum analysis calculates under sea situations at different levels.
2. the ship movement prediction method according to claim 1 based on Taylor expansion Element BEM, it is characterized in that: institute
The reading grid file stated specifically includes: reading grid file and automatically extracts ship waterline information, in conjunction with flow field matching boundary intelligence
Intelligent parameter and waterline information automatically generate the water surface and matching face discrete grid block of coincidence boundary member method, the ship waterline letter
Breath includes head and the tail stationary point space coordinate, waterline matched curve function；Described carries out ship hydrostatic calculation using gridding information
It specifically includes based on hull discrete grid block, Ship ' hydrostatic force parameter, checks hydrostatic force parameter numerical result and physics ship
The error of parameter, the hydrostatic force parameter include displacement of volume, centre of buoyancy, the centre of floatation, the moment of inertia and wetted surface area.
3. the ship movement prediction method according to claim 1 based on Taylor expansion Element BEM, it is characterized in that institute
Influence coefficient matrix involved in boundary integral equation needed for the calculating Taylor expansion Element BEM stated specifically includes: will float
Discrete body-moisture meter face is several quadrangles or triangular element, on each unit, centered on taking cell node coordinate mean value,
Face element midpoint antithesis pole strength makees Taylor expansion and retains first derivative item, makees Taylor expansion to source strength and only retains first derivative
?；The tangential first derivative for introducing site carrys out Closure equation group, and it is unknown for constituting about dipole intensity, even strong first derivative
Number, source strength are the linear algebraic equation systems of known variables.
4. the ship movement prediction method according to claim 1 based on Taylor expansion Element BEM, it is characterized in that institute
Time domain Green function and its space the normal derivative solution stated specifically include: wave are disturbed using matching method unofficial biography, in matching face
It is upper to construct matching condition using time domain Green function.
5. the ship movement prediction method according to claim 1 based on Taylor expansion Element BEM, it is characterized in that: step
Corresponding folded mould gesture in rapid 3,4,5,6,9, the instantaneous item first part of radiation potential, second part, radiation potential memory term, diffraction gesture and
Its space derivation utilizes Taylor expansion Element BEM to solve.
6. the ship movement prediction method according to claim 1 based on Taylor expansion Element BEM, it is characterized in that: step
When corresponding radiation potential memory term and diffraction gesture impulse response function time domain solve in rapid 6 and 9, Free Face Conditions use DB lattice
Formula.
7. the ship movement prediction method according to claim 1 based on Taylor expansion Element BEM, it is characterized in that: step
When corresponding radiation potential memory term and diffraction gesture impulse response function time domain solve in rapid 6 and 9, Free Face Conditions are using integral lattice
Formula.
8. the ship movement prediction method according to claim 1 based on Taylor expansion Element BEM, it is characterized in that: step
Corresponding folded Model Potential in rapid 3,4,5, the corresponding boundary integral equation of the instantaneous item of radiation potential utilize GMRES (m) iterative method to ask
Solution.
9. the ship movement prediction method according to claim 1 based on Taylor expansion Element BEM, it is characterized in that: step
The boundary integral equation solved with diffraction gesture is radiated in rapid 6 and 9, and time stepping solution is carried out using matrix inversion method.
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| CN113111603A (en) * | 2021-04-07 | 2021-07-13 | 哈尔滨工程大学 | Double-floating-body platform wave excitation force and motion response forecasting method |
| CN113127797A (en) * | 2021-04-30 | 2021-07-16 | 华南理工大学 | Hydrodynamic semi-analytic algorithm for wave energy floating body with irregular bottom shape heaving |
| CN113127797B (en) * | 2021-04-30 | 2023-02-14 | 华南理工大学 | Hydrodynamic semi-analysis method for wave energy floating body with irregular bottom shape heaving |
| CN115495919A (en) * | 2022-09-30 | 2022-12-20 | 中国船舶科学研究中心 | Numerical solution method of time domain gentle slope equation based on lattice Boltzmann |
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